Daily Practice - Higher Plus

The point (7, 24) lies on the circle x² + y² = 625. Work out the gradient of the tangent to the circle at that point.The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.

A bag holds 6 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?

A block has mass 790 g (to the nearest 10 g) and volume 6 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 790 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Use the iteration x(n+1) = cube root of (6x(n) + 2) with x(0) = 1. Work out x(1) to 3 decimal places.